Problem 6 Find all functions f:R→Rf:\mathbb{R}\to \mathbb{R}f:R→R such that for all real numbers a,b,a,b,a,b, and ccc : (i) If a+b+c≥0a+b+c\ge 0a+b+c≥0 then f(a3)+f(b3)+f(c3)≥3f(abc).f(a^3)+f(b^3)+f(c^3)\ge 3f(abc).f(a3)+f(b3)+f(c3)≥3f(abc). (ii) If a+b+c≤0a+b+c\le 0a+b+c≤0 then f(a3)+f(b3)+f(c3)≤3f(abc).f(a^3)+f(b^3)+f(c^3)\le 3f(abc).f(a3)+f(b3)+f(c3)≤3f(abc). Proposed by Ashwin Sah